The monoid of families of quiver representations

Details The monoid of families of quiver representations The monoid of families of quiver representations

2001-05-15

arxiv.org/abs/math/0105121v1

Mathematics

Rings and Algebras

27 pages

Scientific paper

A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting interactions between representation theory, algebraic geometry and quantum group theory. For example, it produces a wealth of interesting examples of families of quiver representations, which can be analyzed by representation theoretic and geometric methods. Conversely, results from representation theory, in particular A. Schofield's work on general properties of quiver representations, allow us to relate the monoid to certain degenerate forms of quantized enveloping algebras.

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